GATE ME 2022 Set 1 — Question 51
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Engineering Mechanics → Dynamics → Dynamics of Rigid Bodies
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Question
A cylindrical disc of mass and radius was spinning at when it was placed on a flat horizontal surface and released (refer to the figure). Gravity acts vertically downwards as shown in the figure. The coefficient of friction between the disc and the surface is finite and positive. Disregarding any other dissipation except that due to friction between the disc and the surface, the horizontal velocity of the center of the disc, when it starts rolling without slipping, will be _________ m/s (round off to 2 decimal places).
Correct answer
0.24 to 0.26
Solution
We use the principle of conservation of angular momentum about the point of contact on the ground, as the friction force passes through this point.
Initial angular momentum:
Final angular momentum (rolling without slipping, ):
By conservation of angular momentum, :The final horizontal velocity is:
Initial angular momentum:
Final angular momentum (rolling without slipping, ):
By conservation of angular momentum, :The final horizontal velocity is:
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